Various Possible Forms of Absolute-Type Ferroelectro-Incommensurateness

Abstract

Phases that are incommensurate but yet also ferroelectric are possible. A ferroelectric incommensurate phase of the absolute type is defined as an incommensurate phase in which the relation P=f(|Q_α|², |Q_β|², |Q_γ|²,…) holds and which has P₀≠0 through this relation. Here P denotes a polarization component; P₀ is its spatial average; Q_α, Q_α^*, Q_β etc. compose a degenerate set of order parameters; f is a function of only the absolute magnitudes (not depending on the arguments) of the order parameters. No possible specific forms of the above function have been known, except the simplest form P=J(|Q_α|²−|Q_β|²), where J is a mere coefficient. The present paper shows a variety of specific forms and the cases where they occur. Some of these cases are particularly discussed.